Differential problems with the Riesz derivative in space are widely used to model anomalous diffusion. Although Riesz–Caputo is more suitable for modeling real phenomena, there few examples literature where numerical methods solve such differential problems. In this paper, we propose approximate of a given function cubic spline. As far as aware, first time that splines have been context derivat...

Two piecewise Hermite bicubic orthogonal spline collocation schemes are considered for the approximate solution of elliptic, self-adjoint, nonhomogeneous Dirichlet boundary value problems on rectangles. In the rst scheme, the nonhomogeneous Dirichlet boundary condition is approximated by means of the piecewise Hermite cubic interpolant, while the piecewise cubic interpolant at the boundary Gaus...

The behavior of the non-linear-coupled systems arising in axially symmetric hydromagnetics flow between two horizontal plates in a rotating system is analyzed, where the lower is a stretching sheet and upper is a porous solid plate. The equations of conservation of mass and momentum are transformed to a system of coupled nonlinear ordinary differential equations. These equations for the velocit...

In this paper, we study polynomial spline collocation methods applied to a particular class of integral-algebraic equations of Volterra type. We analyse mixed systems of second and first kind integral equations. Global convergence and local superconvergence results are established.

In the first part of this paper we study the regularity properties of solutions to initial or boundary-value problems of Fredholm integro-differential equationswithweakly singular or other nonsmooth kernels.We then use these results in the analysis of a piecewise polynomial collocation method for solving such problems numerically. Presented numerical examples display that theoretical results ar...

Efficient numerical algorithms are developed and analyzed that implement symmetric multilevel preconditioners for the solution of an orthogonal spline collocation (OSC) discretization of a Dirichlet boundary value problem with a non–self-adjoint or an indefinite operator. The OSC solution is sought in the Hermite space of piecewise bicubic polynomials. It is proved that the proposed additive an...

We propose a new iterative algorithm for the retrieval of the microphysical properties of stratospheric and tropospheric aerosols from multiwavelength lidar data. We consider the basic equation as an ill-posed problem and solve the system derived from spline collocation via a Padé iteration. The algorithm takes special care of the fact that the reconstruction of the distribution via spline coll...

In this paper we study the numerical solution of nonlinear Volterra integrodifferential equations with infinite delay by spline collocation and related Runge-Kutta type methods. The kernel function in these equations is of the form k(t,s,y(t),y(s)), with a representative example given by Volterra's population equation, where we have k(t, s, y(t),y(s)) = a(t s) ■ G(y(t), y(s)). '

The aim of this paper is to carry out a rigorous error analysis for the Strang splitting Laguerre–Hermite/Hermite collocation methods for the time-dependent Gross–Pitaevskii equation (GPE). We derive error estimates for full discretizations of the three-dimensional GPE with cylindrical symmetry by the Strang splitting Laguerre–Hermite collocation method, and for the d-dimensional GPE by the Str...